Catastrophe Theory and the Problem of Stellar Collapse

Casti, J.L. (1974). Catastrophe Theory and the Problem of Stellar Collapse. IIASA Research Memorandum. IIASA, Laxenburg, Austria: RM-74-028

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Abstract

Recently, a new mathematical tool called "catastrophe theory" has been developed by the topologists Thom, Zeeman, Mather, and others in an attempt to mathematically explain the discontinuities of observed behavior due to smooth changes in the basic parameters of physical, social, and biological processes. It has been shown that the number of mathematically distinct ways in which such discontinuities may arise is small when compared with the dimension of the process, and a complete classification of all distinct types has been made for processes depending upon five or less parameters.

The purpose of this note is two-fold: first, to serve as a very brief introduction to the subject of catastrophe theory and secondly, to illustrate the theory by applying it to the determination of equilibrium configurations for stellar matter which has reached the endpoint of thermonuclear evolution, the problem of "stellar collapse". It will be seen that catastrophe theory enables us to give a very satisfactory explanation for the observed phenomenon of unstable equilibrium configurations and the appearance of the so-called Chandrasekhar and Oppenheimer-Landau-Volkoff crushing points.

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